Deep learning predicts path-dependent plasticity

Significance We show that material plasticity can be precisely and efficiently predicted by deep-learning methods. This approach is fundamentally different from the century-old theory of continuum plasticity because it is not iteratively tracing the yield surface, neither does it require the notion of effective strain or stress at the macroscopic level. Instead, we use representative computer simulations of materials, including microstructure and constituents, load them along different deformation paths, and then learn the reversible, irreversible, and history-dependent phenomena directly from data. We demonstrate that complex phenomena such as distortional hardening can be predicted within 0.5% error. The generality of the methodology and widespread importance of plasticity in designing structures and materials make it useful to a myriad of fields. Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress–strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.